Engineering Lung-Inspired Flow Field Geometries for Electrochemical Flow Cells with Stereolithography 3D Printing

Electrochemical flow reactors are increasingly relevant platforms in emerging sustainable energy conversion and storage technologies. As a prominent example, redox flow batteries, a well-suited technology for large energy storage if the costs can be significantly reduced, leverage electrochemical reactors as power converting units. Within the reactor, the flow field geometry determines the electrolyte pumping power required, mass transport rates, and overall cell performance. However, current designs are inspired by fuel cell technologies but have not been engineered for redox flow battery applications, where liquid-phase electrochemistry is sustained. Here, we leverage stereolithography 3D printing to manufacture lung-inspired flow field geometries and compare their performance to conventional flow field designs. A versatile two-step process based on stereolithography 3D printing followed by a coating procedure to form a conductive structure is developed to manufacture lung-inspired flow field geometries. We employ a suite of fluid dynamics, electrochemical diagnostics, and finite element simulations to correlate the flow field geometry with performance in symmetric flow cells. We find that the lung-inspired structural pattern homogenizes the reactant distribution throughout the porous electrode and improves the electrolyte accessibility to the electrode reaction area. In addition, the results reveal that these novel flow field geometries can outperform conventional interdigitated flow field designs, as these patterns exhibit a more favorable balance of electrical and pumping power, achieving superior current densities at lower pressure loss. Although at its nascent stage, additive manufacturing offers a versatile design space for manufacturing engineered flow field geometries for advanced flow reactors in emerging electrochemical energy storage technologies.

Section S1 -CAD drawings and determination of the electrolyte exchange perimeter ( ) Figure S1: CAD drawings of the printed flow fields together with the dimensions of the channel levels, channels depth and inlet/outlet holes.
To calculate the electrolyte exchange perimeter, an average is taken between the inner ( Figure S2a) and outer ( Figure S2b) perimeter, excluding the outer edges close to the cell border.  Section S2 -Materials and chemicals Figure S3: Cell configuration for the pressure drop experiments. Figure S4: Single-electrolyte cell configuration for the electrochemical experiments and cell components.

Section S3 -Reproducibility study of electrochemical experiments
To estimate the reproducibility of the polarization and impedance experiments, seven different cells were tested with the ID flow field in combination with the carbon paper electrode. The fresh materials (electrodes, membrane and electrolytes) were replaced between experiments.

S4b -Species concentration at the electrode surface
To calculate the concentration of species at the surface of the electrode, the mass transfer flux of Fe 2+ and Fe 3+ species from the electrolyte bulk to the electrode surface is modeled by assuming a linear Nernst diffusion layer: where j refers exclusively to the redox species Fe 2+ and Fe 3+ .
Substituting using Eq. (10) in the main article, yields a system of two linear equations whose solution gives the species concentrations as: where the value of km is assumed the same for the oxidized (O) and reduced (R) redox species, and the coefficients A and B are given by:

S4c -Estimation of the electrolyte potential at the electrode-membrane interface
The electrolyte potential at the membrane interface can be estimated considering a voltage loss across the membrane of ΔΦ 1 : Where is the ionic current passing through the membrane and the membrane resistance, which can be calculated from the membrane conductivity as: where and are the membrane thickness and cross-sectional area, respectively, and is the membrane conductivity. This results in a membrane resistance value of 0.0356 Ω calculated with the data from Table S2. The liquid potential at the membrane interface is calculated following the next steps: 1. An arbitrary value of Vcell = 0.3 V is chosen for the estimation of Φ for the ID case 2. Give a random value to Φ at membrane. E.g. 0 V for Vcell = 0.3 V 3. Simulation → obtain = 573.6 A m -2 * 2.55 ×10 -4 m -2 = 0.146 A 4. Calculation of Φ (Eq. S6) = ΔΦ = 0.146 * 0.0356 = 5.41×10 -3 V = 5.52 mV S8

S4d -Mesh independence analysis
The mesh independence analysis was performed at Vcell = 0.1 V and 3.5 cm s -1 electrolyte velocity. As observed from Table S3 and Figure S7 an stable solution is achieved after 4 000 000 number of elements, which is reflected in the monitorization of the current density and on the 2D concentration profiles of Fe 3+ .  Figure S7: Mesh independence analysis: the response in the total current density from the electrochemical flow cell is evaluated with different number of elements in the mesh.

S4e -Validation of the numerical model
The model was successfully validated for the three flow field designs at an electrolyte velocity of 3.5 cm s -1 . The cell polarization curves were evaluated experimentally and compare to the model predictions. Since the model formulation does not include the ohmic losses from the flow fields contact resistance, we corrected the cell polarization predictions using the measured ohmic resistance, i.e., 0.496 Ω cm 2 for the printed flow field (Figure 2b) in the empty cell where the two flow fields are stacked together ( Figure  S11b).  The electrochemically active surface area of the electrode was estimated by charging the double layer in a flow cell setup as illustrated in Figure S4, using the graphite interdigitated flow field. To do so, a supporting electrolyte of 2 M HCl in water was used to avoid the occurrence of faradaic processes. A linear electrolyte velocity of 5 cm s -1 was used and cyclic voltammetry was performed between -0.2 V and 0.2 V at 5 different scan rates (20, 50, 100, 150, and 200 mV s -1 ). The specific capacitance of glassy carbon (18 μF cm -2 4 ) was used to estimate the ECSA based on prior literature. 5,6 A typical voltammetry result, representative for the rest of the data in the study, is shown in Figure S9. From the cyclic voltammetry measurements, the average capacitive current can be extracted at 0 V for each of the scan rates. Subsequently, the electrochemical double layer capacitance (EDLC) can be extracted from the slope of the corresponding linear fit, according to the following equation 7 : = (S8) S11 Figure S10. Linear fitting of the average capacitive current at different scan rates to obtain the EDLC from the slope.

Section S6-Conductivity calculation of graphite and printed flow fields
Two different cell configurations were used as explained in Figure S11 to estimate the total ohmic resistance in the regular cell with all components (Figure S11a) and exclusively of the flow fields to isolate the ohmic resistance coming from the flow fields due to the different graphite or printed materials ( Figure  S11b). The electrical conductivity of the flow fields (Table S4) was calculated from the ohmic resistance measured in the empty flow cell setup with only the flow fields ( Figure S11b). Electrochemical impedance spectroscopy measurements were performed following the same procedure as explained in the methodology section of the manuscript, and the high-frequency intercept was taken as the ohmic resistance value for the conductivity estimation according to where σ FF is the electrical conductivity [S m -1 ], A the contact area (taken as that of the electrode 2.55 cm 2 ), L the thickness the sample (2 x flow field thickness (3.18 mm)) and R the measured resistance from EIS [Ω]. S13 Table S4: Conductivity values of the graphite and printed flow fields estimated from an empty cell with only the flow fields stacked together.

Conductivity [S m -1 ]
Graphite flow field 318 Printed flow field 128 Section S7 -Hydraulic analysis: apparent permeability and Forchheimer equation fits

Section S8 -Limiting current measurements
To capture the effect of flow field geometry on the mass transfer polarization region, limiting current measurements were performed to estimate later the volume-specific surface area mass transfer coefficients. Figure S12 shows an example of limiting current measurements which are achieved after 0.3 V of applied cell potential.
Figure S12: Limiting current measurements at an electrolyte velocity of 1.5 cm s -1 .

Section S9 -Volume-specific surface area mass transfer coefficient vs. pressure drop
In Figure S13 a comparison between the volume-specific surface area mass transfer coefficients against the corresponding pressure losses is presented for the three flow fields. No significant differences were observed due to the higher flow rates required by lung-inspired flow fields driven by their high electrolyte exchange perimeter. Figure S13: Volume-specific surface area mass transfer coefficients obtained from limiting current measurements over a range of pressure drop normalized by the electrode length (1.7 cm) corresponding to the different studied electrolyte velocities. S15 Section S10 -Electrochemical impedance spectroscopy fittings Figure S14. Equivalent circuit model for electrochemical impedance spectroscopy.
The Z fittings are made based on the average PEIS data of the experiments (2-3 repetitions) using E Z-fit tool in the software EC-lab V11.33.